Nuclear Magnetic Resonance Phenomenon
Atomic nuclei possessing a spin quantum number larger than zero have a non-classical angular momentum called “nuclear spin.” Since the nuclei are charged, the nuclear spin creates a nuclear magnetic moment. In the presence of an external magnetic field, a slight majority of these magnetic moments are aligned parallel with the field. This “excess population” of aligned spins or “polarization” is the target for nuclear magnetic resonance (NMR) experiments.
A radio frequency (RF) pulse at exactly the right frequency causes a coherent precession of spin magnetic moments (a “coherence”) about the external magnetic field axis (also called the “longitudinal axis”). The angle that the RF pulse tips the net magnetic moment of the spins away from the longitudinal axis is called the “flip angle” and is usually 90° in an “excitation pulse” or 180° in an “inversion pulse.” If the net magnetic moment has been rotated 90° from the longitudinal axis, it is said to be “transverse.” RF pulses also have a phase associated with them (usually 0°, 90°, 180°, or 270°), which determines which direction the net magnetic moment will be pointing once it reaches the transverse plane.
The precessing magnetic moments produce a free induction decay (FID) signal that can be detected with an RF coil and an RF receiver. The experimental power of NMR lies in the extraordinarily high “Q” (the ratio of stored to dissipated energy per cycle in a dynamic system) in a precessing population of spin ½ magnetic moments due to their weak interaction with the environment. The resulting narrow linewidth allows accurate spatial separation in magnetic resonance imaging and precise measurement of chemical shifts in high resolution NMR spectroscopy.
Magnetic Resonance Imaging and Spatial Selectivity
The NMR phenomenon is exploited in a medical imaging modality called magnetic resonance imaging (MRI). In this technique, a part of the (human) body is placed in a large (usually superconducting) magnet. RF transmission and reception is used to excite and receive NMR signals from 1H nuclei in the body (primarily those present in water). The relaxation rates of the detected signals vary with the type of tissue the nuclei are embedded in. Special techniques are used to localize the RF signals in space and the result is a detailed anatomical picture of the imaged region. Current MRI images depict planes of tissue only a few millimeters thick and have in-plane resolution of less than a millimeter.
A key tool for signal localization in MRI is a set of 3-axis “pulsed magnetic field gradients.” These gradients can be rapidly switched on and off and produce a variation in the magnetic field strength that is linear in a certain direction (usually labeled as x, y, and z). During the application of a gradient, the resonance frequency of the NMR signal is, thus, a linear function of the position along the axis of that gradient. In MRI, these gradients are applied in different ways to achieve spatial localization in each of the three spatial dimensions (Mansfield et al., NMR Imaging in Biomedicine Academic Press, San Diego (1982)).
In the first dimension (which can be an arbitrary plane in three dimension), spatial localization is achieved during RF excitation. A linear pulsed field gradient known as the “slice select gradient” is applied simultaneously with the application of the RF excitation pulse as shown in FIG. 1. The “temporal” shape of the pulse defines the “excitation profile” in the frequency domain. The effect of the linear field gradient is to map the frequency domain “excitation profile” into position in space along the gradient, creating a “spatial profile.” The result is that the “spatial excitation profile” is to first order the Fourier transform of the temporal RF pulse shape. Usually a (sin(t)/t) or “sinc” shaped RF pulse is used, which results in excitation of a narrow planar slice of the body, since the Fourier transform of (sin(t)/t) is a rectangle. The excitation gradient is applied during the duration of the shaped RF pulse. Since the gradient shifts the resonance frequency of the spins proportionally to their position in the gradient, the RF pulse is “off-resonance” or not quite at the correct frequency for all spins except those in the exact center of the gradient. An off-resonance RF pulse leads to a phase shift proportional to the frequency offset. This shift can be approximated by assuming an on-resonance pulse followed by an evolution period of duration,tau=2*(pulse width)/piduring which time phase evolves due to the frequency offset (Cavanagh et al., Protein NMR Spectroscopy, Academic Press, San Diego (1996)). The frequency offset of each spin is proportional to its position in the selection gradient direction. Therefore, the phase shift resulting from the selective excitation is also proportional to position. The result is a linear phase shift in the direction of the gradient. This shift can be removed by reversing the gradient for the period tau, during which transverse magnetization is present (FIG. 1).
Once a thin plane of material has been excited, the radio receiver is turned on and RF signals from the precessing spins are detected with a receiver. During this period, a linear magnetic field gradient known as the “readout” or “frequency encoding” gradient is applied in a direction orthogonal to the slice select gradient. The signal frequency of each spin is proportional to its localized magnetic field strength and, thus, is proportional to its position in the gradient direction (i.e., X). A Fourier transform of the received time domain signals then separates the signals by position in the readout gradient direction (FIG. 2). The implementation of the readout gradient is shown in FIG. 3. After excitation, the phase of the signal from each part of the sample is the same. A “readout dephase” gradient pulse imparts a phase shift as a function of position. The readout gradient then causes frequency encoding which acts to rephase the phase shift. In the middle of the acquisition window, the signal peaks because signals from the entire sample are instantaneously in-phase.
The same method is used to localize in the final, third dimension. In this case, rather than apply a continuous gradient pulse as in the readout direction, a short gradient pulse known as the “phase encoding” gradient is applied in the third direction in the time between RF excitation and reception. The entire experiment is repeated many times with the phase encoding gradient strength (amplitude times duration) incremented linearly as a function of experiment number. The net result is again that a Fourier transform of the received time domain signals, this time in the direction associated with repeated experiments, results in localization in the third direction. Simultaneous application of all three of these techniques provides a detailed two-dimensional (2D) picture of a thin slice of tissue. FIG. 4 shows a schematic of the basic spatial encoding scheme used in MRI.
A slight modification of the technique described above, which allows acquisition of an entire 2D slice in a single experiment, is called “echo planar imaging.” In this technique, the readout gradient is stronger, thereby compressing the spatial encoding of the second direction in time. During each gradient pulse, the transverse magnetization across the sample is gradually rephased, producing a signal peak or “gradient echo.” Fourier transform of the gradient echo produces a spatial profile of the signal in the gradient direction. The gradient is then reversed and rephased again from the opposite direction. Thus, a “square wave oscillating” gradient will generate a train of gradient recalled echoes in the center of each gradient pulse. The phase encoding gradient can then be applied in short pulses between these echoes, allowing acquisition of an entire 2D image in a single transient. FIG. 5 shows a schematic of the spatial encoding scheme for echo planar MRI.
High Resolution Nuclear Magnetic Resonance Spectroscopy
Like MRI, high resolution NMR relies on the phenomenon of magnetic resonance in order to obtain spectral information from NMR active (usually spin ½) atomic nuclei. However, in the case of conventional high resolution NMR, signals are not spatially resolved. Instead, experiments are employed that gather detailed information about the localized chemical environment of the nuclei in a molecule, as well as the spatial interaction of their magnetic moments. High resolution NMR is conducted on samples in solution and each atomic nucleus in the molecule resonates at a slightly different frequency or “chemical shift.” The chemical shift provides information about the molecular environment of the atom and allows, in conjunction with their mutual coupling, one to assign signals to specific nuclei.
NMR active nuclei that are covalently bonded in a molecule interact by a mechanism known as “scalar coupling” in which one nucleus causes a frequency shift (+ or −½ of the scalar coupling constant depending on the spin state of the atom) to the NMR frequency of the other nucleus. Scalar coupling can be exploited to transfer polarization from one nucleus to the next. Polarization can be transferred to the same type of atom (i.e., 1H to 1H) in a “homonuclear” NMR experiment or to another type of atom (i.e., 1H to 15N) in a “heteronuclear” NMR experiment.
A pulse sequence module known as “insensitive nuclei enhanced by polarization transfer” or INEPT is used to transfer polarization from an NMR sensitive spin such as 1H to a less sensitive spin such as 15N. “Multidimensional heteronuclear NMR” studies use this module repeatedly to sequentially transfer polarization. The experiment is repeated with different time delays or “chemical shift evolution periods” in order to gather chemical shift information on each of the involved spins. RF pulse sequences have been designed that exploit the known covalent structure of proteins and provide chemical shifts for hydrogens, carbons, and nitrogens in proteins that have been labeled with the spin ½ isotopes 13C and 15N. The chemical shifts can be combined with signals from another type of study that produces signals from pairs of protons that are close in space to solve the three dimensional structure of biological macromolecules.
NMR RF pulse sequences often rely on “RF pulse phase cycling” to suppress artifacts, to detect signals in indirect dimensions in a phase-sensitive manner (“quadrature detection”), to select desired coherence transfer pathways as in double quantum filtered (DQF) correlation spectroscopy (COSY), and/or to edit signals into sub-spectra of a G-matrix Fourier transform (GFT) NMR experiment. Phase cycling consists of repeating the same sequence of RF pulses two or more times while changing the phase(s) of one or more RF pulses and/or the receiver phase (Ernst et al., Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon, Oxford (1987)).
Historically, NMR experiments are repeated many times so that “signal averaging” can be used to increase the signal to noise ratio. If such signal averaging is required to achieve a sufficiently high signal-to-noise ratio, an NMR experiment is considered “sensitivity limited” (Szyperski et al., “Reduced-Dimensionality NMR Spectroscopy for High-Throughput Protein resonance Assignment,” Proc. Natl. Acad. Sci. USA 99:8009-8014 (2002)). The desire to obtain complete chemical shift assignments for protein amino acid residues has led to the development of two-, three-, and even four-dimensional NMR experiments requiring the acquisition of hundreds or even thousands of free induction decays (FIDs) in order to sample the indirect chemical shift evolution periods. When using a highly sensitive NMR spectroscopic set-up, this may lead to the situation where NMR time is solely invested to sample indirect dimensions and not for achieving a sufficient signal-to-noise ratio. This data acquisition regime is named the “sampling limited regime” (Szyperski et al., “Reduced-Dimensionality NMR Spectroscopy for High-Throughput Protein Resonance Assignment,” Proc. Natl. Acad. Sci. USA 99:8009-8014 (2002)).
Several approaches have been developed to decrease data collection time while still obtaining high-dimensional NMR spectral information. GFT NMR spectroscopy (Kim et al., “GFT NMR, A New Approach to Rapidly Obtain Precise High-Dimensional NMR Spectral Information,” J Am. Chem. Soc. 125:1385-1393 (2003); Atreya et al., “G-matrix Fourier Transform NMR Spectroscopy for Complete Protein Resonance Assignment,” Proc. Natl. Acad. Sci. U.S.A. 101:9642-9647 (2004)) allows projection of multi-dimensional NMR spectra into fewer dimensional space with associated time savings. In another vein, Frydman et al. have adapted spatially selective excitation from MRI to simultaneously conduct multiple time increments of indirect dimensions of a multidimensional NMR experiment on a sample by dividing the sample into discrete spatial slices (Frydman et al. “Principles and Features of Single-Scan Two-Dimensional NMR Spectroscopy,” J Am. Chem. Soc. 125:9204-9217 (2003); U.S. Pat. No. 6,873,153 to Frydman).
As mentioned above, the combination of higher dimensional studies which require a number of transients to get usable resolution in each dimension, along with improvements in equipment sensitivity, higher field strength magnets and cryogenic probes, has lead to a point where the duration of the data acquisition is determined by sampling needs rather than intrinsic signal to noise limitations. Development of methods for shortening this duration while retaining the required NMR spectral information is an active area of research. Reduced dimensionality and GFT NMR spectroscopy (Szyperski et al., “GFT NMR, A New Approach to Rapidly Obtain Precise High-Dimensional NMR Spectral Information,” J Am. Chem. Soc. 125:1385-1393 (2003)), sparse sampling of NMR data, and Frydman's spatial-temporal approach (Frydman et al., “The Acquisition of Multidimensional NMR Spectra Within a Single Scan,” Proc. Natl. Acad. Sci. U.S.A. 99:15858 (2002)) each address this problem in different ways. Nonetheless, a large need for tools allowing one to reduce the minimal measurement times of multidimensional NMR experiments remains.
The present invention is directed to achieving this objective.